AP Calculus BC : Polar Form

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

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Example Question #165 : Parametric, Polar, And Vector

Rewrite in polar form:

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Polar Form

What is the following coordinate in polar form?

Provide the angle in degrees.

Possible Answers:

Correct answer:

Explanation:

To calculate the polar coordinate, use

However, keep track of the angle here. 68 degree is the mathematical equivalent of the expression, but we know the point (-2,-5) is in the 3rd quadrant, so we have to add 180 to it to get 248.

Some calculators might already have provided you with the correct answer.

.

Example Question #3 : Polar Form

What is the equation  in polar form?

Possible Answers:

Correct answer:

Explanation:

We can convert from rectangular form to polar form by using the following identities:  and . Given , then .

. Dividing both sides by ,

 

Example Question #4 : Polar Form

What is the equation  in polar form?

Possible Answers:

None of the above

Correct answer:

Explanation:

We can convert from rectangular form to polar form by using the following identities:  and . Given , then . Multiplying both sides by ,

Example Question #2 : Polar Form

Convert the following function into polar form:

Possible Answers:

Correct answer:

Explanation:

The following formulas were used to convert the function from polar to Cartestian coordinates:

Note that the last formula is a manipulation of a trignometric identity.

Simply replace these with x and y in the original function.

Example Question #14 : Parametric, Polar, And Vector Functions

What is the equation  in polar form?

Possible Answers:

Correct answer:

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities:  and . Given , then:

 Dividing both sides by , we get:

Example Question #15 : Parametric, Polar, And Vector Functions

What is the polar form of ?

Possible Answers:

Correct answer:

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: and . Given , then:

Dividing both sides by , we get:

Example Question #16 : Parametric, Polar, And Vector Functions

What is the polar form of ?

Possible Answers:

None of the above

Correct answer:

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: and . Given , then:

 

 

Example Question #17 : Parametric, Polar, And Vector Functions

What is the polar form of ?

Possible Answers:

None of the above

Correct answer:

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: and . Given , then:

Dividing both sides by , we get:

Example Question #3 : Polar Form

What is the polar form of ?

Possible Answers:

None of the above

Correct answer:

Explanation:

We can convert from rectangular to polar form by using the following trigonometric identities: and . Given , then:

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